A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems
Please always quote using this URN:urn:nbn:de:0296-matheon-12950
- This paper studies the relationship between the material derivative method, the shape derivative method, the min-max formulation of Correa and Seeger, and the Lagrange method introduced by Cea. A theorem is formulated which allows a rigorous proof of the shape differentiability without the usage of material derivative; the domain expression is automatically obtained and the boundary expression is easy to derive. Furthermore, the theorem is applied to a cost function which depends on a quasi-linear transmission problem. Using a Gagliardo penalization the existence of optimal shapes is established.